Analysis for SSFA project: Two factor model

Filtered weakly by < 20% NMP

Table of contents

1. Used packages
2. Global settings
3. Load data
4. Model specification
5. Inference
   1. epLsar
   2. R²
   3. Asfc
   4. Smfc
   5. HAsfc9
6. Summary

Used packages

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns; sns.set()
import pickle
import arviz as az
import pymc3 as pm

from matplotlib.colors import to_rgb

import scipy.stats as stats 

from IPython.display import display

import matplotlib as mpl

%load_ext autoreload
%autoreload 2

import plotting_lib

Global settings

Output

writeOut = True
outPathPlots = "../plots/statistical_model_two_factors_filter_weak/"
outPathData = "../derived_data/statistical_model_two_factors_filter_weak/"
prefix = "TwoFactor_filter_weak"

Plotting

widthMM = 190 
widthInch = widthMM / 25.4
ratio = 0.66666
heigthInch = ratio*widthInch

SMALL_SIZE = 8
MEDIUM_SIZE = 10
BIGGER_SIZE = 12

plt.rc('font', size=SMALL_SIZE)          # controls default text sizes
plt.rc('axes', titlesize=SMALL_SIZE)     # fontsize of the axes title
plt.rc('axes', labelsize=MEDIUM_SIZE)    # fontsize of the x and y labels
plt.rc('xtick', labelsize=SMALL_SIZE)    # fontsize of the tick labels
plt.rc('ytick', labelsize=SMALL_SIZE)    # fontsize of the tick labels
plt.rc('legend', fontsize=SMALL_SIZE)    # legend fontsize
plt.rc('figure', titlesize=BIGGER_SIZE)  # fontsize of the figure title
sns.set_style("ticks")

dpi = 300

sizes = [SMALL_SIZE,MEDIUM_SIZE,BIGGER_SIZE]

Computing

numSamples = 1000
numCores = 4
numTune = 1000
numPredSamples = 2000
random_seed=36534535
target_accept = 0.99

Load data

datafile = "../derived_data/preprocessing/preprocessed_filter_weak.dat"

with open(datafile, "rb") as f:
    x1,x2,_,df,dataZ,dictMeanStd,dictTreatment,dictSoftware = pickle.load(f)    

Show that everything is correct:

display(pd.DataFrame.from_dict({'x1':x1,'x2':x2}))

	x1	x2
0	0	5
1	1	5
2	0	5
3	1	5
4	0	5
...	...	...
273	1	9
274	0	9
275	1	9
276	0	9
277	1	9

278 rows × 2 columns

x1 indicates the software used, x2 indicates the treatment applied.

for surfaceParam,(mean,std) in dictMeanStd.items():
    print("Surface parameter {} has mean {} and standard deviation {}".format(surfaceParam,mean,std))

Surface parameter epLsar has mean 0.0032388209205305753 and standard deviation 0.0019378273835719989
Surface parameter Rsquared has mean 0.9974096825435252 and standard deviation 0.007283582118542012
Surface parameter Asfc has mean 14.919474245449283 and standard deviation 12.47068676838922
Surface parameter Smfc has mean 1.155270960424856 and standard deviation 7.13503174525663
Surface parameter HAsfc9 has mean 0.44593694325514915 and standard deviation 0.7912033512620836
Surface parameter HAsfc81 has mean 0.9300206156734742 and standard deviation 2.3638534390774013

for k,v in sorted(dictTreatment.items(), key=lambda x: x[0]):    
    print("Number {} encodes treatment {}".format(k,v))

Number 0 encodes treatment BrushDirt
Number 1 encodes treatment BrushNoDirt
Number 2 encodes treatment Clover
Number 3 encodes treatment Clover+dust
Number 4 encodes treatment Control
Number 5 encodes treatment Dry bamboo
Number 6 encodes treatment Dry grass
Number 7 encodes treatment Dry lucerne
Number 8 encodes treatment Grass
Number 9 encodes treatment Grass+dust
Number 10 encodes treatment RubDirt

for k,v in dictSoftware.items():
    print("Number {} encodes software {}".format(k,v))

Number 0 encodes software ConfoMap
Number 1 encodes software Toothfrax

display(dataZ)

	index	TreatmentNumber	SoftwareNumber	DatasetNumber	NameNumber	epLsar_z	Rsquared_z	Asfc_z	Smfc_z	HAsfc9_z	HAsfc81_z
0	0	5	0	0	115	0.608031	0.081494	-0.261684	-0.120632	-0.391977	-0.239736
1	1	5	1	0	115	0.764866	0.295228	-0.368764	-0.145206	-0.392397	-0.240365
2	2	5	0	0	116	1.355641	-0.166422	0.043912	-0.120632	-0.346351	-0.268091
3	3	5	1	0	116	1.350574	0.282460	-0.137943	-0.145206	-0.349727	-0.282929
4	4	5	0	0	117	0.930308	-0.359987	-0.137793	-0.120632	-0.233444	-0.221925
...	...	...	...	...	...	...	...	...	...	...	...
273	273	9	1	2	52	0.611602	0.267769	-1.050437	0.035516	0.493708	0.076860
274	274	9	0	2	53	0.084569	0.197735	-0.966638	-0.093723	0.242115	0.257597
275	275	9	1	2	53	-0.051512	0.319804	-0.975181	-0.143224	0.644288	0.381453
276	276	9	0	2	54	-1.041990	0.284041	-1.077552	0.011489	-0.095103	-0.053253
277	277	9	1	2	54	-1.308590	0.336005	-1.081522	-0.104672	-0.126169	-0.038105

278 rows × 11 columns

display(df)

	Dataset	Name	Software	Diet	Treatment	Before.after	NMP	NMP_cat	epLsar	Rsquared	Asfc	Smfc	HAsfc9	HAsfc81	NewEplsar	TreatmentNumber	SoftwareNumber	DatasetNumber	NameNumber
0	GuineaPigs	capor_2CC6B1_txP4_#1_1_100xL_1	ConfoMap	Dry bamboo	Dry bamboo	NaN	0.717312	0-5%	0.004417	0.998003	11.656095	0.294557	0.135803	0.363319	0.019460	5	0	0	115
1	GuineaPigs	capor_2CC6B1_txP4_#1_1_100xL_1	Toothfrax	Dry bamboo	Dry bamboo	NaN	0.717312	0-5%	0.004721	0.999560	10.320730	0.119219	0.135471	0.361833	NaN	5	1	0	115
2	GuineaPigs	capor_2CC6B1_txP4_#1_1_100xL_2	ConfoMap	Dry bamboo	Dry bamboo	NaN	1.674215	0-5%	0.005866	0.996198	15.467083	0.294557	0.171903	0.296292	0.020079	5	0	0	116
3	GuineaPigs	capor_2CC6B1_txP4_#1_1_100xL_2	Toothfrax	Dry bamboo	Dry bamboo	NaN	1.674215	0-5%	0.005856	0.999467	13.199232	0.119219	0.169232	0.261217	NaN	5	1	0	116
4	GuineaPigs	capor_2CC6B1_txP4_#1_1_100xL_3	ConfoMap	Dry bamboo	Dry bamboo	NaN	1.760409	0-5%	0.005042	0.994788	13.201101	0.294557	0.261235	0.405422	0.019722	5	0	0	117
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
273	Sheeps	L8-Ovis-90730-lm2sin-a	Toothfrax	Grass+dust	Grass+dust	NaN	0.000000	0-5%	0.004424	0.999360	1.819802	1.408678	0.836560	1.111706	NaN	9	1	2	52
274	Sheeps	L8-Ovis-90764-lm2sin-a	ConfoMap	Grass+dust	Grass+dust	NaN	0.000000	0-5%	0.003403	0.998850	2.864831	0.486556	0.637499	1.538943	0.018978	9	0	2	53
275	Sheeps	L8-Ovis-90764-lm2sin-a	Toothfrax	Grass+dust	Grass+dust	NaN	0.000000	0-5%	0.003139	0.999739	2.758297	0.133366	0.955699	1.831721	NaN	9	1	2	53
276	Sheeps	L8-Ovis-90814-lm2sin-a	ConfoMap	Grass+dust	Grass+dust	NaN	0.000000	0-5%	0.001220	0.999479	1.481662	1.237247	0.370691	0.804138	0.017498	9	0	2	54
277	Sheeps	L8-Ovis-90814-lm2sin-a	Toothfrax	Grass+dust	Grass+dust	NaN	0.000000	0-5%	0.000703	0.999857	1.432148	0.408433	0.346111	0.839946	NaN	9	1	2	54

278 rows × 19 columns

Model specification

class TwoFactorModel(pm.Model):
    
    """
    Compute params of priors and hyperpriors.
    """
    def getParams(self,x1,x2,y):
        # get lengths
        Nx1Lvl = np.unique(x1).size
        Nx2Lvl = np.unique(x2).size
                        
        dims = (Nx1Lvl, Nx2Lvl)
        
        ### get standard deviations
        
        # convert to pandas dataframe to use their logic
        df = pd.DataFrame.from_dict({'x1':x1,'x2':x2,'y':y})
        
        s1 = df.groupby('x1').std()['y'].max()
        s2 = df.groupby('x2').std()['y'].max()
                
        stdSingle = (s1, s2)
        
        prefac = 0.05
        s12 = prefac * np.linalg.norm([s1,s2])
        
        stdMulti = (s12)
        
        return (dims, stdSingle, stdMulti)
    
    def printParams(self,x1,x2,y):
        dims, stdSingle, stdMulti = self.getParams(x1,x2,y)
        Nx1Lvl, Nx2Lvl = dims
        s1, s2 = stdSingle
        s12 = stdMulti
        
        print("The number of levels of the x variables are {}".format(dims))
        print("The standard deviations used for the beta priors are  {}".format(stdSingle))
        print("The standard deviations used for the M12 priors are {}".format(stdMulti))
    
    def __init__(self,name,x1,x2,y,model=None):
        
        # call super's init first, passing model and name
        super().__init__(name, model)
        
        # get parameter of hyperpriors
        dims, stdSingle, stdMulti = self.getParams(x1,x2,y)
        Nx1Lvl, Nx2Lvl = dims
        s1, s2 = stdSingle
        s12 = stdMulti
        
        ### hyperpriors ### 
        # observation hyperpriors
        lamY = 1/30.
        muGamma = 0.5
        sigmaGamma = 2.
        
        # prediction hyperpriors
        sigma0 = pm.HalfNormal('sigma0',sd=1)
        sigma1 = pm.HalfNormal('sigma1',sd=s1, shape=Nx1Lvl)       
        sigma2 = pm.HalfNormal('sigma2',sd=s2, shape=Nx2Lvl)
        beta2 = (np.sqrt(6)*sigma2)/(np.pi)
        
        mu_b0 = pm.Normal('mu_b0', mu=0., sd=1)
        mu_b1 = pm.Normal('mu_b1', mu=0., sd=1, shape=Nx1Lvl)        
        mu_b2 = pm.Normal('mu_b2', mu=0., sd=1, shape=Nx2Lvl)       
        
        sigma12 = pm.HalfNormal('sigma12',sd=s12)
                               
        ### priors ### 
        # observation priors        
        nuY = pm.Exponential('nuY',lam=lamY)
        sigmaY = pm.Gamma('sigmaY',mu=muGamma, sigma=sigmaGamma)
        
        # prediction priors
        b0_dist = pm.Normal('b0_dist', mu=0, sd=1)
        b0 = pm.Deterministic("b0", mu_b0 + b0_dist * sigma0)
       
        b1_dist = pm.Normal('b1_dist', mu=0, sd=1)
        b1 = pm.Deterministic("b1", mu_b1 + b1_dist * sigma1)
                        
        b2_beta = pm.HalfNormal('b2_beta', sd=beta2, shape=Nx2Lvl)
        b2_dist = pm.Gumbel('b2_dist', mu=0, beta=1)
        b2 = pm.Deterministic("b2", mu_b2 + b2_beta * b2_dist)
        
        mu_M12 = pm.Normal('mu_M12', mu=0., sd=1, shape=[Nx1Lvl, Nx2Lvl])
        M12_dist = pm.Normal('M12_dist', mu=0, sd=1)
        M12 = pm.Deterministic("M12", mu_M12 + M12_dist * sigma12)
        
        #### prediction ###         
        mu = pm.Deterministic('mu',b0 + b1[x1]+ b2[x2] +  M12[x1,x2] )
                                        
        ### observation ### 
        y = pm.StudentT('y',nu = nuY, mu=mu, sd=sigmaY, observed=y)

Inference

epLsar

with pm.Model() as model:
    epLsarModel = TwoFactorModel('epLsar',x1,x2,dataZ.epLsar_z.values)

Verify model settings

epLsarModel.printParams(x1,x2,dataZ.epLsar_z.values)

The number of levels of the x variables are (2, 11)
The standard deviations used for the beta priors are  (1.0181033807478441, 1.4891257020651163)
The standard deviations used for the M12 priors are 0.09019464854470463

try:
    graph_epLsar = pm.model_to_graphviz(epLsarModel)    
except:
    graph_epLsar = "Could not make graph"
graph_epLsar

Check prior choice

with epLsarModel as model:
    prior_pred_epLsar = pm.sample_prior_predictive(samples=numPredSamples,random_seed=random_seed)

plotting_lib.plotPriorPredictive(widthInch,heigthInch,dpi,writeOut,outPathPlots,df,dictMeanStd,\
                                 prior_pred_epLsar,dataZ.epLsar_z.values,'epLsar',prefix)

Prior choice is as intended: Broad over the data range.

Sampling

with epLsarModel as model:
    trace_epLsar = pm.sample(numSamples,cores=numCores,tune=numTune,max_treedepth=20, init='auto',target_accept=0.99,random_seed=random_seed)

Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [epLsar_M12_dist, epLsar_mu_M12, epLsar_b2_dist, epLsar_b2_beta, epLsar_b1_dist, epLsar_b0_dist, epLsar_sigmaY, epLsar_nuY, epLsar_sigma12, epLsar_mu_b2, epLsar_mu_b1, epLsar_mu_b0, epLsar_sigma2, epLsar_sigma1, epLsar_sigma0]

100.00% [8000/8000 02:57<00:00 Sampling 4 chains, 0 divergences]

Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 178 seconds.

with epLsarModel as model:
    if writeOut:
        with open(outPathData + '{}_model_{}.pkl'.format(prefix,'epLsar'), 'wb') as buff:
            pickle.dump({'model':epLsarModel, 'trace': trace_epLsar}, buff)            

Save for later comparison

if writeOut:
    np.save('../derived_data/statistical_model_two_factors_filter_weak/statistical_model_two_factors_filter_weak_epLsar_oldb1', trace_epLsar['epLsar_b1'])
    np.save('../derived_data/statistical_model_two_factors_filter_weak/statistical_model_two_factors_filter_weak_epLsar_oldb2', trace_epLsar['epLsar_b2'])
    np.save('../derived_data/statistical_model_two_factors_filter_weak/statistical_model_two_factors_filter_weak_epLsar_oldM12', trace_epLsar['epLsar_M12'])

Check sampling

with epLsarModel as model:
    dataTrace_epLsar = az.from_pymc3(trace=trace_epLsar)

pm.summary(dataTrace_epLsar,hdi_prob=0.95).round(2)

	mean	sd	hdi_2.5%	hdi_97.5%	mcse_mean	mcse_sd	ess_mean	ess_sd	ess_bulk	ess_tail	r_hat
epLsar_mu_b0	-0.05	0.82	-1.65	1.54	0.01	0.02	6470.0	1562.0	6473.0	2593.0	1.0
epLsar_mu_b1[0]	0.04	0.73	-1.46	1.38	0.01	0.01	5416.0	1540.0	5398.0	2587.0	1.0
epLsar_mu_b1[1]	-0.07	0.74	-1.55	1.36	0.01	0.01	5127.0	1465.0	5139.0	2939.0	1.0
epLsar_mu_b2[0]	-0.15	0.66	-1.45	1.12	0.01	0.01	6447.0	2150.0	6450.0	3472.0	1.0
epLsar_mu_b2[1]	-0.12	0.69	-1.52	1.18	0.01	0.01	5453.0	2235.0	5448.0	2856.0	1.0
...	...	...	...	...	...	...	...	...	...	...	...
epLsar_mu[273]	0.45	0.28	-0.11	0.98	0.00	0.00	3996.0	3777.0	4001.0	3551.0	1.0
epLsar_mu[274]	0.47	0.32	-0.13	1.13	0.00	0.00	4040.0	3810.0	4033.0	3712.0	1.0
epLsar_mu[275]	0.45	0.28	-0.11	0.98	0.00	0.00	3996.0	3777.0	4001.0	3551.0	1.0
epLsar_mu[276]	0.47	0.32	-0.13	1.13	0.00	0.00	4040.0	3810.0	4033.0	3712.0	1.0
epLsar_mu[277]	0.45	0.28	-0.11	0.98	0.00	0.00	3996.0	3777.0	4001.0	3551.0	1.0

382 rows × 11 columns

plotting_lib.plotDiagnostics(widthInch,heigthInch,dpi,writeOut,outPathPlots,trace_epLsar,dataTrace_epLsar,\
                             'epLsar',prefix)

/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/arviz/plots/backends/matplotlib/pairplot.py:216: UserWarning: rcParams['plot.max_subplots'] (40) is smaller than the number of resulting pair plots with these variables, generating only a 8x8 grid
  UserWarning,

with epLsarModel as model:
    plotting_lib.plotTracesB(widthInch,heigthInch,dpi,writeOut,outPathPlots,trace_epLsar,'epLsar',prefix)

with epLsarModel as model:
    plotting_lib.pm.energyplot(trace_epLsar)

Posterior predictive distribution

with epLsarModel as model:
    posterior_pred_epLsar = pm.sample_posterior_predictive(trace_epLsar,samples=numPredSamples,random_seed=random_seed)

/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/sampling.py:1708: UserWarning: samples parameter is smaller than nchains times ndraws, some draws and/or chains may not be represented in the returned posterior predictive sample
  "samples parameter is smaller than nchains times ndraws, some draws "

100.00% [2000/2000 00:01<00:00]

plotting_lib.plotPriorPosteriorPredictive(widthInch,heigthInch,dpi,writeOut,outPathPlots,df,dictMeanStd,\
                                          prior_pred_epLsar,posterior_pred_epLsar,dataZ.epLsar_z.values,\
                                          'epLsar',prefix)

Compare prior and posterior for model parameters

with epLsarModel as model:
    pm_data_epLsar = az.from_pymc3(trace=trace_epLsar,prior=prior_pred_epLsar,posterior_predictive=posterior_pred_epLsar)

arviz.data.io_pymc3 - WARNING - posterior predictive variable epLsar_y's shape not compatible with number of chains and draws. This can mean that some draws or even whole chains are not represented.

plotting_lib.plotPriorPosteriorB(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,\
                                 pm_data_epLsar,'epLsar',prefix)

plotting_lib.plotLevels(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,dictTreatment,\
                        dictSoftware,trace_epLsar,'epLsar',x1,x2)

plotting_lib.plotLevelsStd(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,dictTreatment,\
                           dictSoftware,trace_epLsar,'epLsar',x1,x2)

Posterior and contrasts

plotting_lib.plotPosterior(widthInch,heigthInch,dpi,writeOut,outPathPlots,dictMeanStd,pm_data_epLsar,'epLsar',prefix)

df_hdi_epLsar = plotting_lib.plotTreatmentPosterior(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,\
                                                    dictMeanStd,dictTreatment,dictSoftware,trace_epLsar,\
                                                    'epLsar',x1,x2,prefix)

df_hdi_epLsar

	Treatment_i	Treatment_j	hdi_ConfoMap_2.5%	hdi_ConfoMap_97.5%	isSignificant_on_ConfoMap	hdi_Toothfrax_2.5%	hdi_Toothfrax_97.5%	isSignificant_on_Toothfrax
0	Dry grass	Dry bamboo	-0.004152	-0.002594	True	-0.003996	-0.002397	True
1	Dry lucerne	Dry bamboo	-0.003326	-0.001788	True	-0.003509	-0.002022	True
2	Dry lucerne	Dry grass	0.000057	0.001571	True	-0.000323	0.001235	False
3	BrushNoDirt	BrushDirt	-0.001377	0.002078	False	-0.001797	0.001283	False
4	Control	BrushDirt	-0.001051	0.002062	False	-0.000649	0.002677	False
5	Control	BrushNoDirt	-0.001703	0.001898	False	-0.000599	0.002795	False
6	RubDirt	BrushDirt	-0.000716	0.002956	False	-0.001682	0.001413	False
7	RubDirt	BrushNoDirt	-0.001393	0.002726	False	-0.001327	0.001686	False
8	RubDirt	Control	-0.001339	0.002509	False	-0.002646	0.000660	False
9	Clover+dust	Clover	-0.001123	0.001394	False	-0.000920	0.001698	False
10	Grass	Clover	0.000052	0.003036	True	0.000386	0.003713	True
11	Grass	Clover+dust	-0.000229	0.002855	False	0.000049	0.003324	True
12	Grass+dust	Clover	0.000332	0.003297	True	0.000620	0.003434	True
13	Grass+dust	Clover+dust	0.000167	0.003241	True	0.000285	0.003140	True
14	Grass+dust	Grass	-0.001428	0.002001	False	-0.001697	0.001666	False

plotting_lib.plotTreatmentPosteriorDiff(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,\
                                        dictTreatment,dictSoftware,trace_epLsar,'epLsar',x1,x2,prefix)

if writeOut:
    df_hdi_epLsar.to_csv(outPathData+ '{}_hdi_{}.csv'.format(prefix,'epLsar'))

R²

with pm.Model() as model:
    RsquaredModel = TwoFactorModel('Rsquared',x1,x2,dataZ["Rsquared_z"].values)

Verify model settings

RsquaredModel.printParams(x1,x2,dataZ["Rsquared_z"].values)

The number of levels of the x variables are (2, 11)
The standard deviations used for the beta priors are  (1.364226512794052, 3.833663350609328)
The standard deviations used for the M12 priors are 0.20345815702507086

pm.model_to_graphviz(RsquaredModel)

Check prior choice

with RsquaredModel as model:
    prior_pred_Rsquared = pm.sample_prior_predictive(samples=numPredSamples,random_seed=random_seed)

plotting_lib.plotPriorPredictive(widthInch,heigthInch,dpi,writeOut,outPathPlots,df,dictMeanStd,\
                                 prior_pred_Rsquared,dataZ["Rsquared_z"].values,'Rsquared',prefix)

Sampling

with RsquaredModel as model:
    trace_Rsquared = pm.sample(numSamples,cores=numCores,tune=numTune,max_treedepth=20, init='auto',target_accept=0.99,random_seed=random_seed)

Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [Rsquared_M12_dist, Rsquared_mu_M12, Rsquared_b2_dist, Rsquared_b2_beta, Rsquared_b1_dist, Rsquared_b0_dist, Rsquared_sigmaY, Rsquared_nuY, Rsquared_sigma12, Rsquared_mu_b2, Rsquared_mu_b1, Rsquared_mu_b0, Rsquared_sigma2, Rsquared_sigma1, Rsquared_sigma0]

100.00% [8000/8000 27:04<00:00 Sampling 4 chains, 0 divergences]

Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1625 seconds.

with RsquaredModel as model:
    if writeOut:
        with open(outPathData + '{}_model_{}.pkl'.format(prefix,'Rsquared'), 'wb') as buff:
            pickle.dump({'model': RsquaredModel, 'trace': trace_Rsquared}, buff)

Check sampling

with RsquaredModel as model:
    dataTrace_Rsquared = az.from_pymc3(trace=trace_Rsquared)

pm.summary(dataTrace_Rsquared,hdi_prob=0.95).round(2)

	mean	sd	hdi_2.5%	hdi_97.5%	mcse_mean	mcse_sd	ess_mean	ess_sd	ess_bulk	ess_tail	r_hat
Rsquared_mu_b0	0.09	0.83	-1.56	1.69	0.01	0.01	5090.0	2109.0	5099.0	2890.0	1.0
Rsquared_mu_b1[0]	-0.06	0.74	-1.53	1.34	0.01	0.01	3681.0	2539.0	3669.0	3353.0	1.0
Rsquared_mu_b1[1]	0.10	0.72	-1.36	1.46	0.01	0.01	4328.0	2934.0	4336.0	3441.0	1.0
Rsquared_mu_b2[0]	0.05	0.67	-1.25	1.34	0.01	0.01	3253.0	2383.0	3270.0	3303.0	1.0
Rsquared_mu_b2[1]	0.02	0.67	-1.31	1.26	0.01	0.01	3147.0	2682.0	3155.0	2829.0	1.0
...	...	...	...	...	...	...	...	...	...	...	...
Rsquared_mu[273]	0.30	0.02	0.26	0.33	0.00	0.00	4108.0	4092.0	4103.0	3710.0	1.0
Rsquared_mu[274]	0.22	0.03	0.16	0.27	0.00	0.00	4006.0	3960.0	4006.0	3711.0	1.0
Rsquared_mu[275]	0.30	0.02	0.26	0.33	0.00	0.00	4108.0	4092.0	4103.0	3710.0	1.0
Rsquared_mu[276]	0.22	0.03	0.16	0.27	0.00	0.00	4006.0	3960.0	4006.0	3711.0	1.0
Rsquared_mu[277]	0.30	0.02	0.26	0.33	0.00	0.00	4108.0	4092.0	4103.0	3710.0	1.0

382 rows × 11 columns

plotting_lib.plotDiagnostics(widthInch,heigthInch,dpi,writeOut,outPathPlots,trace_Rsquared,\
                             dataTrace_Rsquared,'Rsquared',prefix)

/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/arviz/plots/backends/matplotlib/pairplot.py:216: UserWarning: rcParams['plot.max_subplots'] (40) is smaller than the number of resulting pair plots with these variables, generating only a 8x8 grid
  UserWarning,

with RsquaredModel as model:
    plotting_lib.plotTracesB(widthInch,heigthInch,dpi,writeOut,outPathPlots,trace_Rsquared,'Rsquared',prefix)

with RsquaredModel as model:
    plotting_lib.pm.energyplot(trace_Rsquared)

Posterior predictive distribution

with RsquaredModel as model:
    posterior_pred_Rsquared = pm.sample_posterior_predictive(trace_Rsquared,samples=numPredSamples,random_seed=random_seed)

/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/sampling.py:1708: UserWarning: samples parameter is smaller than nchains times ndraws, some draws and/or chains may not be represented in the returned posterior predictive sample
  "samples parameter is smaller than nchains times ndraws, some draws "

100.00% [2000/2000 00:01<00:00]

plotting_lib.plotPriorPosteriorPredictive(widthInch,heigthInch,dpi,writeOut,outPathPlots,df,dictMeanStd,\
                                          prior_pred_Rsquared,posterior_pred_Rsquared,\
                                          dataZ["Rsquared_z"].values,'Rsquared',prefix)

Compare prior and posterior for model parameters

with RsquaredModel as model:
    pm_data_Rsquared = az.from_pymc3(trace=trace_Rsquared,prior=prior_pred_Rsquared,posterior_predictive=posterior_pred_Rsquared)

arviz.data.io_pymc3 - WARNING - posterior predictive variable Rsquared_y's shape not compatible with number of chains and draws. This can mean that some draws or even whole chains are not represented.

plotting_lib.plotPriorPosteriorB(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,\
                                 pm_data_Rsquared,'Rsquared',prefix)

plotting_lib.plotLevels(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,\
                        dictTreatment,dictSoftware,trace_Rsquared,'Rsquared',x1,x2)

plotting_lib.plotLevelsStd(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,\
                           dictTreatment,dictSoftware,trace_Rsquared,'Rsquared',x1,x2)

Posterior and contrasts

plotting_lib.plotPosterior(widthInch,heigthInch,dpi,writeOut,outPathPlots,dictMeanStd,\
                           pm_data_Rsquared,'Rsquared',prefix)

df_hdi_R = plotting_lib.plotTreatmentPosterior(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,\
                                               dictTreatment,dictSoftware,trace_Rsquared,'Rsquared',x1,x2,prefix)

df_hdi_R

	Treatment_i	Treatment_j	hdi_ConfoMap_2.5%	hdi_ConfoMap_97.5%	isSignificant_on_ConfoMap	hdi_Toothfrax_2.5%	hdi_Toothfrax_97.5%	isSignificant_on_Toothfrax
0	Dry grass	Dry bamboo	0.000659	0.001970	True	-0.000351	0.000253	False
1	Dry lucerne	Dry bamboo	0.000067	0.001447	True	-0.000407	0.000144	False
2	Dry lucerne	Dry grass	-0.001082	0.000049	False	-0.000384	0.000276	False
3	BrushNoDirt	BrushDirt	-0.001244	0.000215	False	-0.000965	0.000147	False
4	Control	BrushDirt	-0.001290	0.000753	False	-0.000634	0.000352	False
5	Control	BrushNoDirt	-0.000712	0.001349	False	-0.000288	0.000781	False
6	RubDirt	BrushDirt	-0.001629	0.000051	False	-0.001153	0.000118	False
7	RubDirt	BrushNoDirt	-0.001106	0.000574	False	-0.000755	0.000541	False
8	RubDirt	Control	-0.001619	0.000571	False	-0.000955	0.000241	False
9	Clover+dust	Clover	-0.000472	0.000480	False	-0.000234	0.000504	False
10	Grass	Clover	-0.000724	0.000501	False	-0.000771	0.000095	False
11	Grass	Clover+dust	-0.000710	0.000560	False	-0.000889	-0.000103	True
12	Grass+dust	Clover	-0.000485	0.000552	False	-0.000475	0.000304	False
13	Grass+dust	Clover+dust	-0.000508	0.000541	False	-0.000566	0.000135	False
14	Grass+dust	Grass	-0.000535	0.000797	False	-0.000193	0.000637	False

plotting_lib.plotTreatmentPosteriorDiff(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,\
                                        dictTreatment,dictSoftware,trace_Rsquared,'Rsquared',x1,x2,prefix)

if writeOut:
    df_hdi_R.to_csv(outPathData+ '{}_hdi_{}.csv'.format(prefix,'Rsquared'))

Asfc

with pm.Model() as model:
    AsfcModel = TwoFactorModel('Asfc',x1,x2,dataZ["Asfc_z"].values)

Verify model settings

AsfcModel.printParams(x1,x2,dataZ["Asfc_z"].values)

The number of levels of the x variables are (2, 11)
The standard deviations used for the beta priors are  (1.0834504037573414, 1.7347208877727194)
The standard deviations used for the M12 priors are 0.10226340176080734

pm.model_to_graphviz(AsfcModel)

Check prior choice

with AsfcModel as model:
    prior_pred_Asfc = pm.sample_prior_predictive(samples=numPredSamples,random_seed=random_seed)

plotting_lib.plotPriorPredictive(widthInch,heigthInch,dpi,writeOut,outPathPlots,df,dictMeanStd,\
                                 prior_pred_Asfc,dataZ["Asfc_z"].values,'Asfc',prefix)

Prior choice is as intended: Broad over the data range.

Sampling

with AsfcModel as model:
    trace_Asfc = pm.sample(numSamples,cores=numCores,tune=numTune,max_treedepth=20, init='auto',target_accept=0.99,random_seed=random_seed)

Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [Asfc_M12_dist, Asfc_mu_M12, Asfc_b2_dist, Asfc_b2_beta, Asfc_b1_dist, Asfc_b0_dist, Asfc_sigmaY, Asfc_nuY, Asfc_sigma12, Asfc_mu_b2, Asfc_mu_b1, Asfc_mu_b0, Asfc_sigma2, Asfc_sigma1, Asfc_sigma0]

100.00% [8000/8000 09:03<00:00 Sampling 4 chains, 0 divergences]

Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 544 seconds.
The number of effective samples is smaller than 10% for some parameters.

with AsfcModel as model:
    if writeOut:
        with open(outPathData + '{}_model_{}.pkl'.format(prefix,'Asfc'), 'wb') as buff:
            pickle.dump({'model': AsfcModel, 'trace': trace_Asfc}, buff)

Check sampling

with AsfcModel as model:
    dataTrace_Asfc = az.from_pymc3(trace=trace_Asfc)

pm.summary(dataTrace_Asfc,hdi_prob=0.95).round(2)

	mean	sd	hdi_2.5%	hdi_97.5%	mcse_mean	mcse_sd	ess_mean	ess_sd	ess_bulk	ess_tail	r_hat
Asfc_mu_b0	-0.06	0.81	-1.65	1.48	0.01	0.01	4064.0	2319.0	4058.0	3075.0	1.0
Asfc_mu_b1[0]	0.07	0.73	-1.39	1.51	0.01	0.01	3340.0	2543.0	3338.0	2695.0	1.0
Asfc_mu_b1[1]	-0.11	0.73	-1.50	1.32	0.01	0.01	3625.0	2612.0	3630.0	3292.0	1.0
Asfc_mu_b2[0]	1.20	0.76	-0.26	2.66	0.02	0.01	2517.0	2517.0	2652.0	2405.0	1.0
Asfc_mu_b2[1]	0.94	0.73	-0.42	2.39	0.01	0.01	3625.0	3328.0	3631.0	3427.0	1.0
...	...	...	...	...	...	...	...	...	...	...	...
Asfc_mu[273]	-1.05	0.06	-1.17	-0.94	0.00	0.00	4027.0	4000.0	4022.0	3506.0	1.0
Asfc_mu[274]	-1.05	0.06	-1.16	-0.92	0.00	0.00	4220.0	4220.0	4219.0	4065.0	1.0
Asfc_mu[275]	-1.05	0.06	-1.17	-0.94	0.00	0.00	4027.0	4000.0	4022.0	3506.0	1.0
Asfc_mu[276]	-1.05	0.06	-1.16	-0.92	0.00	0.00	4220.0	4220.0	4219.0	4065.0	1.0
Asfc_mu[277]	-1.05	0.06	-1.17	-0.94	0.00	0.00	4027.0	4000.0	4022.0	3506.0	1.0

382 rows × 11 columns

plotting_lib.plotDiagnostics(widthInch,heigthInch,dpi,writeOut,outPathPlots,trace_Asfc,dataTrace_Asfc,'Asfc',prefix)

/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/arviz/plots/backends/matplotlib/pairplot.py:216: UserWarning: rcParams['plot.max_subplots'] (40) is smaller than the number of resulting pair plots with these variables, generating only a 8x8 grid
  UserWarning,

with AsfcModel as model:
    plotting_lib.plotTracesB(widthInch,heigthInch,dpi,writeOut,outPathPlots,trace_Asfc,'Asfc',prefix)

with AsfcModel as model:
    plotting_lib.pm.energyplot(trace_Asfc)

Posterior predictive distribution

with AsfcModel as model:
    posterior_pred_Asfc = pm.sample_posterior_predictive(trace_Asfc,samples=numPredSamples,random_seed=random_seed)

/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/sampling.py:1708: UserWarning: samples parameter is smaller than nchains times ndraws, some draws and/or chains may not be represented in the returned posterior predictive sample
  "samples parameter is smaller than nchains times ndraws, some draws "

100.00% [2000/2000 00:01<00:00]

plotting_lib.plotPriorPosteriorPredictive(widthInch,heigthInch,dpi,writeOut,outPathPlots,df,\
                                          dictMeanStd,prior_pred_Asfc,posterior_pred_Asfc,\
                                          dataZ["Asfc_z"].values,'Asfc',prefix)

plotting_lib.plotLevels(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,dictTreatment,\
                        dictSoftware,trace_Asfc,'Asfc',x1,x2)

plotting_lib.plotLevelsStd(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,dictTreatment,\
                           dictSoftware,trace_Asfc,'Asfc',x1,x2)

Compare prior and posterior for model parameters

with AsfcModel as model:
    pm_data_Asfc = az.from_pymc3(trace=trace_Asfc,prior=prior_pred_Asfc,posterior_predictive=posterior_pred_Asfc)

arviz.data.io_pymc3 - WARNING - posterior predictive variable Asfc_y's shape not compatible with number of chains and draws. This can mean that some draws or even whole chains are not represented.

plotting_lib.plotPriorPosteriorB(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,\
                                 pm_data_Asfc,'Asfc',prefix)

Posterior and contrasts

plotting_lib.plotPosterior(widthInch,heigthInch,dpi,writeOut,outPathPlots,dictMeanStd,pm_data_Asfc,'Asfc',prefix)

df_hdi_Asfc = plotting_lib.plotTreatmentPosterior(widthInch,heigthInch,dpi,sizes,writeOut,\
                                                  outPathPlots,dictMeanStd,dictTreatment,dictSoftware,\
                                                  trace_Asfc,'Asfc',x1,x2,prefix)

df_hdi_Asfc

	Treatment_i	Treatment_j	hdi_ConfoMap_2.5%	hdi_ConfoMap_97.5%	isSignificant_on_ConfoMap	hdi_Toothfrax_2.5%	hdi_Toothfrax_97.5%	isSignificant_on_Toothfrax
0	Dry grass	Dry bamboo	-3.916452	2.795973	False	-4.296147	1.377498	False
1	Dry lucerne	Dry bamboo	-4.260454	1.899807	False	-4.704579	0.667324	False
2	Dry lucerne	Dry grass	-2.615826	1.717622	False	-2.195671	1.343382	False
3	BrushNoDirt	BrushDirt	-15.010884	3.380206	False	-13.605707	4.419980	False
4	Control	BrushDirt	-35.731852	4.275047	False	-31.670087	3.675433	False
5	Control	BrushNoDirt	-34.009450	14.409722	False	-30.388298	13.091720	False
6	RubDirt	BrushDirt	-42.757337	-32.042331	True	-35.972142	-23.722769	True
7	RubDirt	BrushNoDirt	-42.529481	-21.978611	True	-36.265074	-14.506282	True
8	RubDirt	Control	-43.365126	-0.792099	True	-36.453023	2.421650	False
9	Clover+dust	Clover	-4.429319	2.363512	False	-4.325436	2.025695	False
10	Grass	Clover	-5.539381	1.270810	False	-5.413694	0.927516	False
11	Grass	Clover+dust	-3.510605	1.055924	False	-3.020075	1.235952	False
12	Grass+dust	Clover	-6.448750	0.127469	False	-6.012465	0.356649	False
13	Grass+dust	Clover+dust	-4.200499	0.142961	False	-3.783693	0.366821	False
14	Grass+dust	Grass	-3.274366	1.239253	False	-2.811040	1.448578	False

plotting_lib.plotTreatmentPosteriorDiff(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,\
                                        dictTreatment,dictSoftware,trace_Asfc,'Asfc',x1,x2,prefix)

if writeOut:
    df_hdi_Asfc.to_csv(outPathData+ '{}_hdi_{}.csv'.format(prefix,'Asfc'))

Smfc

with pm.Model() as model:
    SmfcModel = TwoFactorModel('Smfc',x1,x2,dataZ.Smfc_z.values)

Verify model settings

SmfcModel.printParams(x1,x2,dataZ.Smfc_z.values)

The number of levels of the x variables are (2, 11)
The standard deviations used for the beta priors are  (1.2903046708375803, 3.554940942907768)
The standard deviations used for the M12 priors are 0.18909317313924404

pm.model_to_graphviz(SmfcModel)

Check prior choice

with SmfcModel as model:
    prior_pred_Smfc = pm.sample_prior_predictive(samples=numPredSamples,random_seed=random_seed)

plotting_lib.plotPriorPredictive(widthInch,heigthInch,dpi,writeOut,outPathPlots,df,dictMeanStd,\
                                 prior_pred_Smfc,dataZ.Smfc_z.values,'Smfc',prefix)

Prior choice is as intended: Broad over the data range.

Sampling

with SmfcModel as model:
    trace_Smfc = pm.sample(numSamples,cores=numCores,tune=numTune,max_treedepth=20, init='auto',target_accept=0.99,random_seed=random_seed)

Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [Smfc_M12_dist, Smfc_mu_M12, Smfc_b2_dist, Smfc_b2_beta, Smfc_b1_dist, Smfc_b0_dist, Smfc_sigmaY, Smfc_nuY, Smfc_sigma12, Smfc_mu_b2, Smfc_mu_b1, Smfc_mu_b0, Smfc_sigma2, Smfc_sigma1, Smfc_sigma0]

10.11% [809/8000 00:12<01:49 Sampling 4 chains, 0 divergences]

---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
~/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/sampling.py in _mp_sample(draws, tune, step, chains, cores, chain, random_seed, start, progressbar, trace, model, callback, discard_tuned_samples, mp_ctx, pickle_backend, **kwargs)
   1485             with sampler:
-> 1486                 for draw in sampler:
   1487                     trace = traces[draw.chain - chain]

~/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/parallel_sampling.py in __iter__(self)
    491         while self._active:
--> 492             draw = ProcessAdapter.recv_draw(self._active)
    493             proc, is_last, draw, tuning, stats, warns = draw

~/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/parallel_sampling.py in recv_draw(processes, timeout)
    351         pipes = [proc._msg_pipe for proc in processes]
--> 352         ready = multiprocessing.connection.wait(pipes)
    353         if not ready:

/usr/lib/python3.7/multiprocessing/connection.py in wait(object_list, timeout)
    919             while True:
--> 920                 ready = selector.select(timeout)
    921                 if ready:

/usr/lib/python3.7/selectors.py in select(self, timeout)
    414         try:
--> 415             fd_event_list = self._selector.poll(timeout)
    416         except InterruptedError:

KeyboardInterrupt: 

During handling of the above exception, another exception occurred:

ValueError                                Traceback (most recent call last)
<ipython-input-97-4de91012caf3> in <module>
      1 with SmfcModel as model:
----> 2     trace_Smfc = pm.sample(numSamples,cores=numCores,tune=numTune,max_treedepth=20, init='auto',target_accept=0.99,random_seed=random_seed)

~/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/sampling.py in sample(draws, step, init, n_init, start, trace, chain_idx, chains, cores, tune, progressbar, model, random_seed, discard_tuned_samples, compute_convergence_checks, callback, return_inferencedata, idata_kwargs, mp_ctx, pickle_backend, **kwargs)
    543         _print_step_hierarchy(step)
    544         try:
--> 545             trace = _mp_sample(**sample_args, **parallel_args)
    546         except pickle.PickleError:
    547             _log.warning("Could not pickle model, sampling singlethreaded.")

~/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/sampling.py in _mp_sample(draws, tune, step, chains, cores, chain, random_seed, start, progressbar, trace, model, callback, discard_tuned_samples, mp_ctx, pickle_backend, **kwargs)
   1510     except KeyboardInterrupt:
   1511         if discard_tuned_samples:
-> 1512             traces, length = _choose_chains(traces, tune)
   1513         else:
   1514             traces, length = _choose_chains(traces, 0)

~/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/sampling.py in _choose_chains(traces, tune)
   1528     lengths = [max(0, len(trace) - tune) for trace in traces]
   1529     if not sum(lengths):
-> 1530         raise ValueError("Not enough samples to build a trace.")
   1531 
   1532     idxs = np.argsort(lengths)[::-1]

ValueError: Not enough samples to build a trace.

Analysis stopped here because sampling did not converge. As the plot shows, some data points are very far away from the others, which would require the analysis to be based on more heavy-tailed distributions.

HAsfc9

with pm.Model() as model:
    HAsfc9Model = TwoFactorModel('HAsfc9',x1,x2,dataZ["HAsfc9_z"].values)

Verify model settings

HAsfc9Model.printParams(x1,x2,dataZ["HAsfc9_z"].values)

The number of levels of the x variables are (2, 11)
The standard deviations used for the beta priors are  (1.2742199511468122, 3.5115369692183998)
The standard deviations used for the M12 priors are 0.18677880213027476

pm.model_to_graphviz(HAsfc9Model)

Check prior choice

with HAsfc9Model as model:
    prior_pred_HAsfc9 = pm.sample_prior_predictive(samples=numPredSamples,random_seed=random_seed)

plotting_lib.plotPriorPredictive(widthInch,heigthInch,dpi,writeOut,outPathPlots,df,dictMeanStd,\
                                 prior_pred_HAsfc9,dataZ["HAsfc9_z"].values,'HAsfc9',prefix)

Prior choice is as intended: Broad over the data range.

Sampling

with HAsfc9Model as model:
    trace_HAsfc9 = pm.sample(numSamples,cores=numCores,tune=numTune,max_treedepth=20, init='auto',target_accept=0.99,random_seed=random_seed)

Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [HAsfc9_M12_dist, HAsfc9_mu_M12, HAsfc9_b2_dist, HAsfc9_b2_beta, HAsfc9_b1_dist, HAsfc9_b0_dist, HAsfc9_sigmaY, HAsfc9_nuY, HAsfc9_sigma12, HAsfc9_mu_b2, HAsfc9_mu_b1, HAsfc9_mu_b0, HAsfc9_sigma2, HAsfc9_sigma1, HAsfc9_sigma0]

100.00% [8000/8000 14:52<00:00 Sampling 4 chains, 0 divergences]

Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 892 seconds.

with HAsfc9Model as model:
    if writeOut:
        with open(outPathData + '{}_model_{}.pkl'.format(prefix,'HAsfc9'), 'wb') as buff:
            pickle.dump({'model': HAsfc9Model, 'trace': trace_HAsfc9}, buff)

Check sampling

with HAsfc9Model as model:
    dataTrace_HAsfc9 = az.from_pymc3(trace=trace_HAsfc9)

pm.summary(dataTrace_HAsfc9,hdi_prob=0.95).round(2)

	mean	sd	hdi_2.5%	hdi_97.5%	mcse_mean	mcse_sd	ess_mean	ess_sd	ess_bulk	ess_tail	r_hat
HAsfc9_mu_b0	-0.06	0.84	-1.81	1.49	0.01	0.01	4513.0	1991.0	4527.0	2921.0	1.0
HAsfc9_mu_b1[0]	-0.01	0.74	-1.39	1.48	0.01	0.01	3933.0	2226.0	3929.0	2942.0	1.0
HAsfc9_mu_b1[1]	-0.04	0.74	-1.51	1.42	0.01	0.01	4126.0	2501.0	4125.0	3332.0	1.0
HAsfc9_mu_b2[0]	-0.13	0.66	-1.46	1.15	0.01	0.01	3202.0	2835.0	3195.0	3082.0	1.0
HAsfc9_mu_b2[1]	-0.07	0.67	-1.38	1.21	0.01	0.01	3094.0	2469.0	3090.0	3108.0	1.0
...	...	...	...	...	...	...	...	...	...	...	...
HAsfc9_mu[273]	-0.18	0.06	-0.28	-0.06	0.00	0.00	4055.0	3970.0	4041.0	3683.0	1.0
HAsfc9_mu[274]	-0.15	0.07	-0.29	-0.02	0.00	0.00	3918.0	3610.0	3927.0	3528.0	1.0
HAsfc9_mu[275]	-0.18	0.06	-0.28	-0.06	0.00	0.00	4055.0	3970.0	4041.0	3683.0	1.0
HAsfc9_mu[276]	-0.15	0.07	-0.29	-0.02	0.00	0.00	3918.0	3610.0	3927.0	3528.0	1.0
HAsfc9_mu[277]	-0.18	0.06	-0.28	-0.06	0.00	0.00	4055.0	3970.0	4041.0	3683.0	1.0

382 rows × 11 columns

plotting_lib.plotDiagnostics(widthInch,heigthInch,dpi,writeOut,outPathPlots,trace_HAsfc9,\
                             dataTrace_HAsfc9,'HAsfc9',prefix)

/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/arviz/plots/backends/matplotlib/pairplot.py:216: UserWarning: rcParams['plot.max_subplots'] (40) is smaller than the number of resulting pair plots with these variables, generating only a 8x8 grid
  UserWarning,

with HAsfc9Model as model:
    plotting_lib.plotTracesB(widthInch,heigthInch,dpi,writeOut,outPathPlots,trace_HAsfc9,'HAsfc9',prefix)

with HAsfc9Model as model:
    plotting_lib.pm.energyplot(trace_HAsfc9)

Posterior predictive distribution

with HAsfc9Model as model:
    posterior_pred_HAsfc9 = pm.sample_posterior_predictive(trace_HAsfc9,samples=numPredSamples,random_seed=random_seed)

/home/bob/Documents/Projekt_Neuwied/SSFA/ssfa-env/lib/python3.7/site-packages/pymc3/sampling.py:1708: UserWarning: samples parameter is smaller than nchains times ndraws, some draws and/or chains may not be represented in the returned posterior predictive sample
  "samples parameter is smaller than nchains times ndraws, some draws "

100.00% [2000/2000 00:01<00:00]

plotting_lib.plotPriorPosteriorPredictive(widthInch,heigthInch,dpi,writeOut,outPathPlots,df,dictMeanStd,\
                                          prior_pred_HAsfc9,posterior_pred_HAsfc9,dataZ["HAsfc9_z"].values,\
                                          'HAsfc9',prefix)

plotting_lib.plotLevels(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,dictTreatment,\
                        dictSoftware,trace_HAsfc9,'HAsfc9',x1,x2)

plotting_lib.plotLevelsStd(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,dictTreatment,\
                           dictSoftware,trace_HAsfc9,'HAsfc9',x1,x2)

Compare prior and posterior for model parameters

with HAsfc9Model as model:
    pm_data_HAsfc9 = az.from_pymc3(trace=trace_HAsfc9,prior=prior_pred_HAsfc9,posterior_predictive=posterior_pred_HAsfc9)

arviz.data.io_pymc3 - WARNING - posterior predictive variable HAsfc9_y's shape not compatible with number of chains and draws. This can mean that some draws or even whole chains are not represented.

plotting_lib.plotPriorPosteriorB(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,\
                                 pm_data_HAsfc9,'HAsfc9',prefix)

Posterior and contrasts

plotting_lib.plotPosterior(widthInch,heigthInch,dpi,writeOut,outPathPlots,dictMeanStd,pm_data_HAsfc9,'HAsfc9',prefix)

df_hdi_HAsfc9 = plotting_lib.plotTreatmentPosterior(widthInch,heigthInch,dpi,sizes,writeOut,\
                                                    outPathPlots,dictMeanStd,dictTreatment,dictSoftware,\
                                                    trace_HAsfc9,'HAsfc9',x1,x2,prefix)

df_hdi_HAsfc9

	Treatment_i	Treatment_j	hdi_ConfoMap_2.5%	hdi_ConfoMap_97.5%	isSignificant_on_ConfoMap	hdi_Toothfrax_2.5%	hdi_Toothfrax_97.5%	isSignificant_on_Toothfrax
0	Dry grass	Dry bamboo	-0.010268	0.143011	False	-0.010625	0.126663	False
1	Dry lucerne	Dry bamboo	-0.049642	0.073424	False	-0.043776	0.064924	False
2	Dry lucerne	Dry grass	-0.133646	0.031096	False	-0.122211	0.028118	False
3	BrushNoDirt	BrushDirt	-0.125128	0.238569	False	-0.140860	0.229987	False
4	Control	BrushDirt	-0.020567	0.415332	False	-0.066013	0.448612	False
5	Control	BrushNoDirt	-0.120627	0.368658	False	-0.139664	0.449018	False
6	RubDirt	BrushDirt	-0.106453	0.178762	False	-0.142743	0.149182	False
7	RubDirt	BrushNoDirt	-0.209790	0.142115	False	-0.242017	0.174436	False
8	RubDirt	Control	-0.368504	0.063584	False	-0.482366	0.066704	False
9	Clover+dust	Clover	-0.132341	0.158945	False	-0.086217	0.173111	False
10	Grass	Clover	-0.286952	0.065272	False	-0.128695	0.125433	False
11	Grass	Clover+dust	-0.281473	0.032155	False	-0.168734	0.086427	False
12	Grass+dust	Clover	-0.319844	0.007649	False	-0.216295	0.043416	False
13	Grass+dust	Clover+dust	-0.300752	-0.021022	True	-0.245888	-0.001685	True
14	Grass+dust	Grass	-0.223490	0.131237	False	-0.206777	0.039294	False

if writeOut:
    df_hdi_HAsfc9.to_csv(outPathData+ '{}_hdi_{}.csv'.format(prefix,'HAsfc9'))

plotting_lib.plotTreatmentPosteriorDiff(widthInch,heigthInch,dpi,sizes,writeOut,outPathPlots,dictMeanStd,\
                                        dictTreatment,dictSoftware,trace_HAsfc9,'HAsfc9',x1,x2,prefix)

Summary

Set the surface parameters for every treatment dataframe:

df_hdi_Asfc["SurfaceParameter"] = "Asfc"
df_hdi_HAsfc9["SurfaceParameter"] = "HAsfc9"
df_hdi_R["SurfaceParameter"] = "R²"
df_hdi_epLsar["SurfaceParameter"] = "epLsar"

df_hdi_total = pd.concat([df_hdi_epLsar,df_hdi_R,df_hdi_Asfc,df_hdi_HAsfc9],ignore_index=True)

Show the treatment pairs and surface parameters where the softwares differ

df_summary = df_hdi_total[df_hdi_total.isSignificant_on_ConfoMap != df_hdi_total.isSignificant_on_Toothfrax][["Treatment_i","Treatment_j","SurfaceParameter","isSignificant_on_ConfoMap","isSignificant_on_Toothfrax","hdi_ConfoMap_2.5%","hdi_ConfoMap_97.5%","hdi_Toothfrax_2.5%","hdi_Toothfrax_97.5%"]]
df_summary

	Treatment_i	Treatment_j	SurfaceParameter	isSignificant_on_ConfoMap	isSignificant_on_Toothfrax	hdi_ConfoMap_2.5%	hdi_ConfoMap_97.5%	hdi_Toothfrax_2.5%	hdi_Toothfrax_97.5%
2	Dry lucerne	Dry grass	epLsar	True	False	0.000057	0.001571	-0.000323	0.001235
11	Grass	Clover+dust	epLsar	False	True	-0.000229	0.002855	0.000049	0.003324
15	Dry grass	Dry bamboo	R²	True	False	0.000659	0.001970	-0.000351	0.000253
16	Dry lucerne	Dry bamboo	R²	True	False	0.000067	0.001447	-0.000407	0.000144
26	Grass	Clover+dust	R²	False	True	-0.000710	0.000560	-0.000889	-0.000103
38	RubDirt	Control	Asfc	True	False	-43.365126	-0.792099	-36.453023	2.421650

if writeOut:
    df_summary.to_csv(outPathData+ 'TwoFactor_summary_filter_weak.csv')

Write out

!jupyter nbconvert --to html Statistical_Model_TwoFactor_filter_weak.ipynb

!jupyter nbconvert --to markdown Statistical_Model_TwoFactor_filter_weak.ipynb